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Stochastic survivable network design problems: Theory and practice

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  • Ljubić, Ivana
  • Mutzel, Petra
  • Zey, Bernd

Abstract

We study survivable network design problems with edge-connectivity requirements under a two-stage stochastic model with recourse and finitely many scenarios. For the formulation in the natural space of edge variables we show that facet defining inequalities of the underlying polytope can be derived from the deterministic counterparts. Moreover, by using graph orientation properties we introduce stronger cut-based formulations. For solving the proposed mixed integer programing models, we suggest a two-stage branch&cut algorithm based on a decomposed model. In order to accelerate the computations, we suggest a new technique for strengthening the decomposed L-shaped optimality cuts which is computationally fast and easy to implement. A computational study shows the benefit of the decomposition and the cut strengthening – which significantly reduces the number of master iterations and the computational running time. Moreover, we evaluate the stability of the scenario generation method and analyze the value of the stochastic solution.

Suggested Citation

  • Ljubić, Ivana & Mutzel, Petra & Zey, Bernd, 2017. "Stochastic survivable network design problems: Theory and practice," European Journal of Operational Research, Elsevier, vol. 256(2), pages 333-348.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:2:p:333-348
    DOI: 10.1016/j.ejor.2016.06.048
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    1. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
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    3. Anupam Gupta & R. Ravi & Amitabh Sinha, 2007. "LP Rounding Approximation Algorithms for Stochastic Network Design," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 345-364, May.
    4. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, February.
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    Cited by:

    1. Markus Leitner & Ivana Ljubić & Martin Luipersbeck & Markus Sinnl, 2018. "Decomposition methods for the two-stage stochastic Steiner tree problem," Computational Optimization and Applications, Springer, vol. 69(3), pages 713-752, April.
    2. Naga V. C. Gudapati & Enrico Malaguti & Michele Monaci, 2022. "Network Design with Service Requirements: Scaling-up the Size of Solvable Problems," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2571-2582, September.

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